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by John L. Cooper III,
Grand Secretary Grand Lodge California

The ritual of the Fellowcraft Degree encourages us to study the "Seven Liberal Arts and Sciences", with particular emphasis placed upon the science of Geometry. Within the short description found in that ritual is hidden a wonderful treasure of Masonic Symbolism. Its careful study will prove quite fruitful for anyone who is desirous of Further Light In Masonry.

The following series of four articles does not pretend to exhaust the subject, but it does aim at suggesting a few lines of Inquiry that may be worth pursuing. Those desirous of more information on Masonic Symbolism may contact Institute for Masonic Studies, Grand Lodge, F. &. A. M. of California, 1111 California Street, San Francisco CA 94108-2284, 415.776.700


Many of our Masonic ideas can be traced back to the Ancient Greek philosopher Pythagoras, who founded a school teaching a "progressive moral science," much like our own. By studying the ideas of the Pythagoreans, we may come to a better appreciation of Freemasonry.

The Pythagoreans were the first to elevate mathematics from purely utilitarian aims to a study worth pursuing for its own sake. Their method was different from that of modern science. They were more concerned with the investigation of principles than with the investigation of thing (1). And unlike our science today, which uses general theories and applies them to specific cases, the Pythagoreans began with a specific phenomenon and attempted to use it to discover universal principles. For the Pythagoreans, the study of Geometry was not so much a separate mathematical discipline, as it was an investigation of the laws which govern the universe itself. (2) And so it is for us as Freemasons.

The heart of their philosophy was the concept of Number, which was described as "the principle, the source and the root of all things." And at the very center of this philosophy was the concept of Monad or Unity: the point. Unity is the principle of all things and the most dominant of all that is: all things emanate from it and it emanates from nothing. It is indivisible and it is everything in power. It is immutable and never departs from its own nature through multiplication (lxl=1). Everything that is intelligible and not yet created exists in it; the nature of ideas, God himself, the soul, the beautiful and the good, and every intelligible essence, such as beauty itself, justice itself, equality itself, for we conceive each of these things as being one and as existing in itself. (3)

The point brings to mind the ideas of initiation and beginning. It also suggests initiative, inception, genesis, originality, unity, singleness, isolation, concentration, self-consciousness and so forth. (4)

As Masons, we are quite familiar with the symbol of the Point Within the Circle. This marvelous device graphically represents the relationship between the individual and the Great Architect of the Universe. It is formed by first placing the point of a compass upon a piece of paper and then circumscribing a circle around that central point. It will be observed that each point of the circle thus traced is equidistant from the central point. Hence, the Great Architect of the Universe, whom we all adore, is omnipresent in our lives. 

Further, the circle represents the boundary line beyond which we should not allow our passions to lead us, lest we lose that unity and common purpose that is so central to our Craft.

The Point Within the Circle is also the alchemical symbol of the Sun. That Sun is the indwelling Spirit within each of us and represents that part of us which our ritual states will "never, never, die." The Sun is the center of our solar system, about which revolve all the planets and (apparently) the signs of the zodiac. It is the source of light and life and was therefore regarded as a symbol of God by the ancients. Even today in modern Freemasonry it is an emblem of the Most High. (5)

This is an important clue to the inner significance of the Master Mason degree, as well. For that degree, when rightly understood, provides a complete summary of the entire Chemical Work. This is not the place to enter into an in depth discussion of that work, but the inquisitive Mason is encouraged to search out this meaning on this own.

There is clearly a great deal of meaning which can be found in even the most simple symbol. We have provided a few clues, but it is up to you to follow them to their logical conclusion. In our next installment, we shall investigate the nature of Duality, represented by a line.


In our first installment, we examined the nature of Unity represented by the Point. From the Point proceeds the Line, representing Duality or the number two. The number 2 signifies duplication, repetition, Wisdom and Science, opposition, polarity, antithesis, succession, sequence, continuation, diffusion, separation, radiation, subordination, dependence, and subconsciousness. (1) The reader would do well to look up each of these words in a dictionary, as doing so will provide many insights into the nature of  Duality. 

The most obvious representation of the number 2 within a Masonic Lodge are the two Brazen Pillars in the northwest corner of the Lodge Room. These pillars are surmounted by globes, a terrestrial globe in the north and a celestial globe in the south. While nothing is mentioned about any such globes in the Old Testament description of King Solomon's Temple, they are important symbolically. The celestial globe represents the essential forces of Nature, the divine origin of creation and the principles by which the universe is governed. Thus, it symbolizes the underlying unity of all.

By contrast, the terrestrial globe represents manifestation, the physical world and the multiplicity of things. The material world proceeds from the divine, just as the line proceeds from the point. The point is finite and limited, but a line contains an infinite number of points within it. The line is therefore unlimited.

The Pythagoreans, an ancient Greek school much like our own Fraternity and the source of much of our Masonic Philosophy, described this idea in terms of Matter (the Indefinite) and Form (Limit). These were "the two most essential elements which are absolutely necessary for the manifestation of phenomenal reality." (2)

If One represents the principle of Unity from which all things arise, then Two, the Dyad, represents Duality, the beginning of multiplicity, the beginning of strife, yet also the possibility of logos, the relation of one thing to another. (3)

In Greek philosophy, the "Logos" was the means by which Creation of the world took place, the "Expression" or "Word" of the Creator. Although Christianity took this phrase over and applied it to Jesus Christ, its use is older and more universal. In Greek philosophy the "Logos" was not only the "act of Creation" itself, but also the means by which Creation took place. In other words, the "Word", or "Expression of God", was responsible for Creation, and was identified with God himself.

An astute reader will not overlook the significance of the Word in our own Masonic allegory. In this sense, it represents knowledge of the Divine. When the Master's "Word" is lost, what is alluded to is the loss of our intimate connection with the Great Architect. The Master Mason is encouraged in our rituals to go in search of that which was lost, to reestablish a conscious connection with the Supreme Being.

The two pillars also establish a line between the outside world and the sacred space inside a Lodge Room. The candidate, when he is brought into a Lodge Room for the first time, is placed between the pillars to reinforce the distinction between these two worlds. And every time we step from the outside world into our Lodge, we should also be reminded of the importance of leaving behind the mundane affairs of the outer world.

Another important idea conveyed by the principle of Duality is that of opposites: Light and Darkness, Black and White, Good and Evil, Male and Female, Order and  Chaos. Within a Lodge Room are many examples of the principle of opposites. The black and white tessellated floor, the sun and the moon, east and west are just some examples.

What is important for us to understand is that these symbols are meant to convey that opposites exist within each of us. Each of us has within himself aspects of Good and aspects of Evil. Our task is to understand and eventually reconcile these opposite forces within ourselves. For in truth, these apparent opposites are actually just different qualities of the same thing.

Good and Evil are really just aspects of the quality of Goodness. Darkness is naught but the absence of Light. We will discuss this idea further in our examination of the Superfice or number 3.


In the first two installments, we looked at two of the symbols used in the Fellow Craft Degree from the Science of Geometry, namely "The Point", and "The Line". In the first article we explored one meaning of "The Point", which was "unity", and the roots of our understanding of this concept from the philosopher Pythagoras was discussed. In "The Line" the concept of duality, or of "opposing forces" was discussed. In both, the Freemason was encouraged to look beyond the obvious symbol, and to apply these meanings within his own life. The same may be said for our discussion of the third concept, "The Superfice".

A "superfice" is a flat plane in geometry. A point has no length or breadth; a line has length, but no breadth; but a superfice has both length and breadth.  If two lines cross each other they create a superfice because together they establish "length" in two directions. A line may be said to be a symbol of infinity, for it extends infinitely in two directions, and (in Euclidean geometry) the ends never meet. It is only when we arrive at the concept of a superfice that we enter what might be said to be the human dimension. A superfice creates a "surface", or more poetically, a "stage", upon which human action can take place.  There are several possible Masonic interpretations of this "stage", but one that is obvious to all who have read the longer form of the First Degree Lecture in our Monitor, is the lodge itself.  The lecture puts it thus: "The form of a lodge is oblong. It extends from East to West and from North to South, and it is said to be thus extensive to denote the universality of Masonry and to teach us that a
Mason's charity should be equally extensive; for in every country and in every clime are Masons to be found."

A Fellow Craft Mason who is properly instructed in one Masonic meaning of "The Superfice" should be caused to reflect on what he heard (or read) as an Entered Apprentice Mason about the Form of the Lodge. The Fellow Craft earns his wages within the Lodge, and in doing so, he must become aware of the two dimensions which constitute it, and which are referenced in the Entered Apprentice Lecture. The first of these Masonic dimensions is "universality".

Freemasonry embraces men of "every country, sect and opinion," and is "one sacred band or society of friends and brothers, among whom no contention should every exist, but that noble contention, or rather emulation, of who best can work and best agree." The first, and primary dimension of a Masonic lodge is that it is universal, and this universality, like one line of the superfice, has no end or boundary. There are no exclusions in Freemasonry because of religion, race, or color.

The second principle, the second dimension making up the "oblong form" of the lodge, is charity, or love. If Freemasonry embraces men of all faiths and all social classes, of all races and all nationalities, then there are no limits on the exercise of Brotherly Love. My obligation to love others as a Freemason extends equally to all, and is without limit. The Fellow Craft is later told that "Geometry [is] the first and noblest of sciences, and the basis upon which the superstructure of Freemasonry is erected." Indeed it is.

The geometric form of the superfice is a symbol of the lodge, where Masonic work begins.  And undergirding our work as Masons must be an understanding that "the superfice", as a part of Geometry, is the plane upon which we carry out our Masonic work. That "plane", symbolized by the lodge itself, reminds us that our charity - our love for the brethren - must be "equally extensive."  And we are further encouraged that we will find co-workers to help us with the Great Work wherever Freemasonry is established, "for in every country and in every clime are Masons to be found."


This is the fourth in a series of discussions on the meaning of geometry, and especially as it is explained in the Lecture of the Fellow Craft Degree.  As we have seen in the three, articles before, the candidate is taught that Freemasonry and geometry are intertwined, and that a proper understanding of geometry is an important is an important means of understanding Freemasonry. Why is this so?  And what can we learn from a study of the principles of geometry that can inform our daily life?

The lectures of the Fellow Craft Degree are not really a short course in geometry. On the surface they seem to imply that a well-educated Fellow Craft ought to know something about the seven liberal arts and sciences, and ought to know more about geometry than about any of the seven. Some writers have assumed that William Preston, who wrote our lectures, was trying to provide a course in education at a time when widespread public education was rare. If so, he went about it in a strange manner, for the lectures do no more than touch upon the subject of science general, and of geometry in particular. Moreover, Preston did not invent the subject matter of his lectures. He merely arranged material in use in the lodges in the 18th century. The association of "geometry" with "Freemasonry" goes back to the Old Charges which pre-date the Grand Lodge era. A manuscript of 1583 stated that geometry ".....teacheth a man the mett and measure of earth and all other things. (Grand Lodge Ms., an edition of the "Old Charges')

Geometry is thus said to be of primary importance to Freemasonry long before William Preston wrote his Illustrations of Masonry in 1772, the source of our current lectures. And if it teaches a man the "measure of .....all other things," then is has to do more with what Man is than what he has learned.

It has to do with the heart, and not with the intellect. This interpretation fits nicely with the explanation of geometry as having to do with a point, a line, a superfice, and a solid. For as a solid has length, breadth, and thickness, so Man, if he is to be whole, must be considered as a totality.

Contemporary psychology has taught us to understand the dysfunctional personality, and this is frequently defined to mean a personality that stresses some character trait at the expense of another. A dysfunctional personality is not "whole". And for Freemasonry itself to be "whole" it has to develop the entire personality. A "whole" Mason is one who develops his mind while developing his spirit. A "whole" Mason is one who recognizes that God is the source of life, and shapes his life in accordance with his understanding of the God that he worships. A "whole" Mason is both inwardly directed, and outwardly directed. He respects himself as a creature of his Creator, and respects the society in which he lives as an outward extension of the "wholeness" of his inner life.

A Fellow Craft Mason who understands the importance of geometry will use the tools of a Fellow Craft Mason to shape his life, in accordance with its principles. And in doing so, will illustrate the meaning of a "solid" in geometry: From a point to a line, from a line to a superfice, and from a superfice to a solid. "Solidity", which we translate as "wholeness", has been attained.


(1) Guthrie, Kenneth Sylvan. The Pythagorean Sourcebook and Library. Grand Rapids, Phanes Press: 1987, p.21


(3) Theon of Smyrna. Mathematics Useful for Understanding Plato. Trans. by R. & D. Lawlor. San Diego, Wizards Bookshelf, 1979. (As quoted in Guthrie)

(4) Case, Paul Foster. Tarot: A Key to the Wisdom of the Ages. Los Angeles, Builders of the Adytum, 1990, p. 8.

(5) Ward, J.S.M. An Interpretation of Our Masonic Symbols. London, A. Lewis: 1956, p. 73.

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